Survey on Semi-Explicit Time Integration of Eddy Current Problems

TL;DR

This survey reviews semi-explicit time integration methods for eddy current problems, focusing on stability, computational efficiency, and recent acceleration techniques to improve simulation performance.

Contribution

It provides a comprehensive overview of semi-explicit time integration approaches, highlighting recent advancements and acceleration methods for magnetoquasistatic field simulations.

Findings

Explicit Euler requires small time steps for stability.

Acceleration methods significantly reduce computation time.

Generalized Schur complement transforms DAEs into ODEs.

Abstract

The spatial discretization of the magnetic vector potential formulation of magnetoquasistatic field problems results in an infinitely stiff differential-algebraic equation system. It is transformed into a finitely stiff ordinary differential equation system by applying a generalized Schur complement. Applying the explicit Euler time integration scheme to this system results in a small maximum stable time step size. Fast computations are required in every time step to yield an acceptable overall simulation time. Several acceleration methods are presented.